Finite Group Databasebeta

← #15833003

Subgroups — #15833003

Order 3328.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124896C211yesmaximal, characteristic
2#13123947C211yesmaximal, characteristic, complemented
3#13123914C211yesmaximal, characteristic, complemented
4#13113711C211yesmaximal, characteristic, complemented
5#13113697C211yesmaximal, characteristic, complemented
6#13113676C211yesmaximal, characteristic, complemented
7#13113662C211yesmaximal, characteristic, complemented
8#13113657C211yesmaximal, characteristic, complemented
9#13113651C211yesmaximal, characteristic, complemented
10#13113633C211yesmaximal, characteristic, complemented
11#13113628C211yesmaximal, characteristic, complemented
12#13113622C211yesmaximal, characteristic, complemented
13#13113236C211yesmaximal, characteristic, complemented
14#13113136C211yesmaximal, characteristic, complemented
15C13×#1488C211yesmaximal, characteristic, complemented
16C4×C13×#41C2211yescharacteristic
17#11719182C2211yescharacteristic
18C13×#432C2211yescharacteristic
19C13×#431C2211yescharacteristic
20#11718899C411yescharacteristic
21#11718899C411yescharacteristic
22#11718688C411yescharacteristic
23C4×#6106C2211yescharacteristic
24C4×#6106C2211yescharacteristic
25Q8×#1055C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27#11718682C411yescharacteristic
28#11718676C411yescharacteristic
29C4×#6104C2211yescharacteristic
30C4×#6104C2211yescharacteristic
31D4×#1055—21no—
32D4×#1055—21no—
33D4×#1055C2211yescharacteristic
34D4×#1055C2211yescharacteristic
35#11718669C411yescharacteristic
36#11718664C411yescharacteristic
37#11718664C411yescharacteristic
38#11718586—21no—
39#11718586C2211yescharacteristic
40#11718586C2211yescharacteristic
41C2×C4⋊#1055—21no—
42C2×C4⋊#1055C2211yescharacteristic
43#11718499C2211yescharacteristic
44#11718499C2211yescharacteristic
45#11718495C2211yescharacteristic
46#11718495C2211yescharacteristic
47#11718388—21no—
48#11718388—21no—
49#11718367—21no—
50#11718367—21no—
51C13×Q8⋊C8C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×D4⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718051C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41C2×C411yescharacteristic
68C2×#6127—21no—
69C4×Q8×C13C2×C411yescharacteristic
70C4×Q8×C13C2311yescharacteristic
71C4×D4×C13—21no—
72C4×D4×C13—21no—
73C4×D4×C13C2×C411yescharacteristic
74C4×D4×C13C2311yescharacteristic
75C13×#117—21no—
76C13×#117C2×C411yescharacteristic
77C2×C42×C13—21no—
78C2×C42×C13C2311yescharacteristic
79C2×#6106C2×C411yescharacteristic
80C2×#6106C2×C411yescharacteristic
81C2×#6104C2×C411yescharacteristic
82C2×#6104C2×C411yescharacteristic
83#88184—21no—
84#88184C2×C411yescharacteristic
85#88184C2×C411yescharacteristic
86C22×#1055—21no—
87C22×#1055—21no—
88C22×#1055—21no—
89C2×#6094—21no—
90C2×#6094—21no—
91C2×C8×D13—21no—
92C2×C8×D13—21no—
93#88129—21no—
94#88128C2×C411yescharacteristic
95C4×D52—21no—
96C4×D52C2311yescharacteristic
97C4×D52C2311yescharacteristic
98#88123C2×C411yescharacteristic
99C13×C4⋊C8—21no—
100C13×C4⋊C8C2311yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×C22⋊C8—21no—
103C13×C22⋊C8—21no—
104C13×#97—21no—
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107#88075C2×C411yescharacteristic
108#88075C2×C411yescharacteristic
109#88072C2×C411yescharacteristic
110#88072C2×C411yescharacteristic
111C22⋊#1055—21no—
112C22⋊#1055—21no—
113C22⋊#1055C2×C411yescharacteristic
114C22⋊#1055C2×C411yescharacteristic
115C22⋊#1055D411yescharacteristic
116C22⋊#1055D411yescharacteristic
117#88060—21no—
118#88060—21no—
119#88060—21no—
120#88060—21no—
121#88049C2×C411yescharacteristic
122#88049C2×C411yescharacteristic
123#88049C2×C411yescharacteristic
124#88049C2×C411yescharacteristic
125#88048C2×C411yescharacteristic
126#88048C2×C411yescharacteristic
127#88047C2×C411yescharacteristic
128#88047C2×C411yescharacteristic
129C4⋊#1055—21no—
130C4⋊#1055—21no—
131C4⋊#1055—21no—
132C4⋊#1055C2×C411yescharacteristic
133C4⋊#1055C2×C411yescharacteristic
134C4⋊#1055D411yescharacteristic
135C4⋊#1055D411yescharacteristic
136C4⋊#1055C2311yescharacteristic
137C4⋊#1055C2311yescharacteristic
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17920—131nomaximal, Sylow
145C13×#41—22no—
146C13×#41—22no—
147C2×Q8×C13C22×C411yescharacteristic
148C2×D4×C13—21no—
149C2×D4×C13C22×C411yescharacteristic
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13#4111yescharacteristic
156C2×C22⋊D13—21no—
157C2×C22⋊D13—21no—
158#6127—81no—
159#6127—81no—
160C2×D52—21no—
161C2×D52—21no—
162C2×D52C22×C411yescharacteristic
163C2×D52C22×C411yescharacteristic
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×Dic26—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4C22×C411yescharacteristic
174C13×C4⋊C4C22×C411yescharacteristic
175C13×C22⋊C4—21no—
176C13×C22⋊C4—21no—
177C13×C22⋊C4—21no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13C22×C411yescharacteristic
182C42×C13C2×D411yescharacteristic
183C42×C13#4111yescharacteristic
184C42×C13C2411yescharacteristic
185#6106—22no—
186#6106—22no—
187#6104—22no—
188#6104—22no—
189#6103—21no—
190#6103—21no—
191#6103—21no—
192#6103—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13C22×C411yescharacteristic
195C4⋊Dic13C22×C411yescharacteristic
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—81no—
199C2×#1055—81no—
200C2×#1055—81no—
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208C2×#1055C2×D411yescharacteristic
209#6094—81no—
210#6094—81no—
211C8×D13—81no—
212C8×D13—81no—
213#3106—131no—
214#2988—131no—
215#2981—131no—
216#1588—131no—
217#1586—131no—
218#1583—131no—
219#1581—131no—
220#1580—131no—
221SD16⋊C8—131no—
222C8×SD16—131no—
223C8×D8—131no—
224#1573—131no—
225#1488D1311yescharacteristic, complemented
226#1480—131no—
227#1454—131no—
228C23×C13—21no—
229C23×C13C4×D411yescharacteristic
230C22×D13—21no—
231C22×D13—21no—
232Q8×C13—21no—
233Q8×C13#13112yes—
234D4×C13—24no—
235D4×C13—21no—
236D4×C13#13112yes—
237C2×C4×C13—24no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—81no—
249C2×C4×C13C4×D411yescharacteristic
250C2×C4×C13C4×D411yescharacteristic
251C2×C4×C13C4×D411yescharacteristic
252C2×C4×C13C23×C411yescharacteristic
253C2×C4×C13C22×D411yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C22⋊D13—81no—
256C22⋊D13—81no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259D52—21no—
260D52—21no—
261D52—21no—
262D52—21no—
263D52—81no—
264D52—81no—
265C4×D13—41no—
266C4×D13—41no—
267C4×D13—41no—
268C4×D13—41no—
269Dic26—81no—
270C8×C13—41no—
271C8×C13—41no—
272C8×C13—41no—
273C8×C13—41no—
274#1055—21no—
275#1055—21no—
276#1055—21no—
277#1055—21no—
278#1055—21no—
279#1055—21no—
280#1055—21no—
281#1055—21no—
282#1055—41no—
283#1055—41no—
284#532—131no—
285C4×#41C2×D1311yescharacteristic
286#482—131no—
287#482—131no—
288#477—131no—
289#476—131no—
290#460—131no—
291#459—131no—
292#449—131no—
293#449—131no—
294C8×Q8—131no—
295C8×Q8—131no—
296C4×SD16—131no—
297C4×SD16—131no—
298C4×D8—131no—
299C4×D8—131no—
300#436—131no—
301#436—131no—
302#435—261no—
303#435—261no—
304C8×D4—131no—
305C8×D4—131no—
306C8×D4—131no—
307C8×D4—131no—
308C8×D4—261no—
309C8×D4—261no—
310#432C2×D1311yescharacteristic
311#431—131no—
312#431—131no—
313#431—261no—
314#431C2×D1311yescharacteristic
315C2×C4⋊C8—131no—
316C2×C4⋊C8—261no—
317#408—261no—
318#408—261no—
319#335—131no—
320#335—131no—
321#334—131no—
322#334—131no—
323Q8⋊C8C2×D1311yescharacteristic
324Q8⋊C8C2×D1311yescharacteristic
325D4⋊C8—131no—
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8C2×D1311yescharacteristic
330D4⋊C8C2×D1311yescharacteristic
331#322—131no—
332#322—131no—
333#322—131no—
334C82—131no—
335C22×C13—21no—
336C22×C13—22no—
337C22×C13—21no—
338C22×C13—21no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13C2×C4×D411yescharacteristic
342C2×D13—41no—
343C2×D13—41no—
344C2×D13—41no—
345C2×D13—41no—
346C2×D13—41no—
347C2×D13—41no—
348C4×C13—21no—
349C4×C13—22no—
350C4×C13—21no—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—41no—
354C4×C13—41no—
355C4×C13C2×#13111yescharacteristic
356C4×C13C2×#13111yescharacteristic
357C4×C13#57611yescharacteristic
358C4×C13#57711yescharacteristic
359Dic13—41no—
360Dic13—41no—
361C2×#41—261no—
362C2×#41C4×D1311yescharacteristic
363C2×SD16—131no—
364C2×SD16—131no—
365C2×D8—131no—
366C2×D8—131no—
367C2×M16—261no—
368C2×M16—261no—
369C22×C8—261no—
370C22×C8—261no—
371C22×C8—261no—
372C22×C8—261no—
373C22×C8—261no—
374C4⋊Q8—131no—
375#127—131no—
376#124—261no—
377#121—131no—
378#121—131no—
379#121—261no—
380C4×Q8C4×D1311yescharacteristic
381C4×Q8C22×D1311yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—131no—
385C4×D4—131no—
386C4×D4—261no—
387C4×D4C4×D1311yescharacteristic
388C4×D4C22×D1311yescharacteristic
389#117—21no—
390#117C4×D1311yescharacteristic
391C2×C42—21no—
392C2×C42C22×D1311yescharacteristic
393#107—131no—
394#107—131no—
395#106—131no—
396#106—131no—
397C4⋊C8—21no—
398C4⋊C8—131no—
399C4⋊C8—131no—
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—131no—
404C4⋊C8—261no—
405C4⋊C8—261no—
406C4⋊C8—261no—
407C4⋊C8C22×D1311yescharacteristic
408C4⋊C8C22×D1311yescharacteristic
409#103—131no—
410#103—131no—
411#102—131no—
412#102—131no—
413#102—131no—
414#102—131no—
415#102—131no—
416#102—131no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—131no—
420C22⋊C8—131no—
421C22⋊C8—131no—
422C22⋊C8—131no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427C22⋊C8—261no—
428C22⋊C8—261no—
429#97—21no—
430C4×C8—131no—
431C4×C8—131no—
432C4×C8—131no—
433C4×C8—131no—
434C4×C8—261no—
435C4×C8—261no—
436C4×C8C22×D1311yescharacteristic
437C4×C8C22×D1311yescharacteristic
438C2×C13—41no—
439C2×C13—42no—
440C2×C13#292911yescharacteristic
441C2×C13#294611yescharacteristic
442C2×C13#295711yescharacteristic
443D13—81no—
444D13—81no—
445#41—22no—
446#41—22no—
447#41—1041no—
448#41—1041no—
449C2×Q8—261no—
450C2×Q8C2×C4×D1311yescharacteristic
451C2×D4—21no—
452C2×D4—131no—
453C2×D4—131no—
454C2×D4—261no—
455C2×D4—261no—
456C2×D4—261no—
457C2×D4—261no—
458C2×D4C2×C4×D1311yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4C2×C4×D1311yescharacteristic
465C22×C4D4×D1311yescharacteristic
466C22×C4#612911yescharacteristic
467SD16—262no—
468SD16—262no—
469D8—262no—
470D8—262no—
471M16—1041no—
472M16—1041no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—131no—
478C2×C8—131no—
479C2×C8—131no—
480C2×C8—131no—
481C2×C8—131no—
482C2×C8—131no—
483C2×C8—131no—
484C2×C8—131no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—1041no—
488C2×C8—1041no—
489C2×C8—1041no—
490C2×C8—1041no—
491C2×C8—1041no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—131no—
495C4⋊C4—131no—
496C4⋊C4—261no—
497C4⋊C4C2×C4×D1311yescharacteristic
498C4⋊C4C2×C4×D1311yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—261no—
503C22⋊C4—261no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42C2×C4×D1311yescharacteristic
510C42D4×D1311yescharacteristic
511C42#612911yescharacteristic
512C42C23×D1311yescharacteristic
513C13#1792011yescharacteristic, complemented, Sylow
514C23—21no—
515C23—261no—
516C23—261no—
517C23#8813511yescharacteristic
518Q8—21no—
519Q8—1041no—
520Q8#8816112yes—
521D4—24no—
522D4—21no—
523D4—261no—
524D4—261no—
525D4—261no—
526D4—261no—
527D4—1041no—
528D4—1041no—
529D4—1041no—
530D4—1041no—
531D4#8816112yes—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4#8813511yescharacteristic
551C2×C4#8813511yescharacteristic
552C2×C4#8813511yescharacteristic
553C2×C4C22×C4×D1311yescharacteristic
554C2×C4C2×D4×D1311yescharacteristic
555C2×C4C2×#612911yescharacteristic
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—261no—
561C8—261no—
562C8—261no—
563C8—261no—
564C8—261no—
565C8—261no—
566C8—261no—
567C8—261no—
568C8—521no—
569C8—521no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—521no—
577C22—521no—
578C22—521no—
579C22—521no—
580C22—521no—
581C22—521no—
582C22C2×#8813511yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—22no—
588C4—41no—
589C4—41no—
590C4—521no—
591C4—521no—
592C4C2×#8816111yescharacteristic
593C4C2×#8816111yescharacteristic
594C4#1171947411yescharacteristic
595C4#1171947511yescharacteristic
596C2—41no—
597C2—42no—
598C2—1041no—
599C2—1041no—
600C2#1312352611yescharacteristic
601C2#1312367111yescharacteristic
602C2#1312374911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1488C2
socleC22×C13C2×C4×D4
prime radical#13124896C2
cosocleC42×C13C24
hypercenter#1488D13
hypocenterC13#17920
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13123947C2semidirect
3. #13123914C2semidirect
4. #13113711C2semidirect
5. #13113697C2semidirect
6. #13113676C2semidirect
7. #13113662C2semidirect
8. #13113657C2semidirect
9. #13113651C2semidirect
10. #13113633C2semidirect
11. #13113628C2semidirect
12. #13113622C2semidirect
13. #13113236C2semidirect
14. #13113136C2semidirect
15. C13×#1488C2semidirect
225. #1488D13semidirect
513. C13#17920semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131248962
#131239472
#131239142
#131137112
#131136972
#131136762
#131136622
#131136572
#131136512
#131136332
#131136282
#131136222
#131132362
#131131362
C13×#14882
#1792013